Do the creatures I summon—like the flame atronach—get stronger when I level up, or do they remain the same regardless of my level or the level of my enemies?
No, the other answer is wrong. The summoned creatures from conjuration are not based on the caster level at all.
All summoned creatures have the same stats (health, damage, etc) regardless of what level you summon them at. The only thing that improves the strength of the summoned creature is the Elemental Potency perk, which boosts all your atronach summons.
If you want a stronger summon, use a higher level spell (such as storm atronach).